Arc-length Method for Frictional Contact with a Criterion of Maximum Dissipation of Energy

An arc-length equilibrium path-following method is proposed for two-dimensional quasi-static frictional contact problems. We consider the Coulomb friction law as well as geometrical nonlinearity. Incorporating a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPCC) in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPCC is proposed, which can be solved by using the conventional nonlinear programming approach. The equilibrium paths of various structures are computed successfully in cases such that there exist some limit points and/or infinite number of successive bifurcation points.